question_answer

A metal rod of Young's modulus Y and coefficient of thermal expansion \[\alpha \] is held at its two ends such that its length remains invariant. If its temperature is raised by \[t{}^\circ C\], the linear stress developed in its is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A) \[\frac{Y}{\alpha t}\]

B) \[Y\alpha t\]

C) \[\frac{1}{(Y\alpha t)}\]

D) \[\frac{\alpha t}{Y}\]

Correct Answer: B

Solution :

                                \[\frac{\Delta \ell }{\ell }=\alpha .\Delta T\]and\[Y=\frac{F/A}{\Delta \ell /\ell }\] So,  \[F=AY\alpha t\] Thermal stress \[\left( \frac{F}{A} \right)=Y\alpha t.\]